If I start a tourney with my Arkham Asylum Guard on the take, can I play him on the up and up in the next game or is that considered changing your team/pieces?

No you can't. They are two different characters on the same dial. So if you add #003a Arkham Asylum Guard to your force during construction then you've commited to that character and cannot change it to #003b Arkham Asylum Guard during the tourney.

That's what I assumed. Thanks.